What type of set is the set of all lines parallel to the x-axis?
Answer and explanation
Correct answer: Infinite set
Every horizontal line has an equation of the form y = c, where c is a real number. Since there are infinitely many possible real values of c, there are infinitely many distinct lines parallel to the x-axis. The x-axis itself is one such line, and lines such as y = 1, y = 2, and y = -3 are other examples. Therefore, the set has infinitely many elements and is an infinite set.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
Every horizontal line has an equation of the form y = c, where c is a real number. Since there are infinitely many possible real values of c, there are infinitely many distinct lines parallel to the x-axis. The x-axis itself is one such line, and lines such as y = 1, y = 2, and y = -3 are other examples. Therefore, the set has infinitely many elements and is an infinite set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
